Question

A fraction becomes 9/11 it 2 is added to
both numerator and denominator . If 3 is
added to both numeratar and denominator it becomes
5/6 find the fraction​

Answer 1

Answer:

7/9

Step-by-step explanation:

suppose fraction is x/y

now given

$\frac{x+2}{y+2} =\frac{9}{11}$

solving it we will get

11x+22=9y+18

11x=9y-4

another thing given is

$\frac{x+3}{y+3} =\frac{5}{6}$

6x+18=5y+15

6x=5y-3

Now to solve the given equation multiply 1st equation by 6 and second one by 11

66x=54y-24

66x=55y-33

so y=9

put value of y in any of the equation,we will get x= 7

so fraction is 7/9

Answer 2

Answer:

Let the numerator and denominator be x and y respectively.

Therefore, the required fraction will be x/y

According to Question now,

➳ (x + 2)/(y + 2) = 9/11

➳ 11(x + 2) = 9(y + 2)

➳ 11x + 22 = 9y + 18

➳ 22 - 18 = 9y - 11x

➳ 4 = 9y - 11x

➳ 11x = 9y - 4

➳ x = 9y - 4/11.......[Equation (i)]

Now, it is given that 3 is added to both numerator and denominator it becomes 5/6 :]

➳ (x + 3)/(y + 3) = 5/6

➳ (x + 3)6 = 5(y + 3)

➳ 6x + 18 = 5y + 15

➳ 6x - 5y + 18 - 15 = 0

➳ 6x - 5y + 3 = 0

➳ 6(9y - 4)/11 - 5y + 3 = 0

➳ 54y - 24/11 = 5y - 3

➳ 54y - 24 = 11(5y - 3)

➳ 54y - 24 = 55y - 33

➳ -24 + 33 = 55y - 54y

➳ 9 = y

Now, Putting y = 9 in equation (i) we get,

➳ x = 9y - 4/11

➳ x = 9(9) - 4/11

➳ x = 81 - 4/11

➳ x = 77/11

➳ x = 7

Therefore, the required fraction is 7/9.